Clique-Width of Point Configurations

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Year of publication 2022
Type Article in Periodical
Magazine / Source Journal of Combinatorial Theory, Ser B
MU Faculty or unit

Faculty of Informatics

Web open access preprint
Keywords point configuration; order type; fixed-parameter tractability; relational structure; clique-width
Description While structural width parameters (of the input) belong to the standard toolbox of graph algorithms, it is not the usual case in computational geometry. As a case study we propose a natural extension of the structural graph parameter of clique-width to geometric point configurations represented by their order type. We study basic properties of this clique-width notion, and show that it is aligned with the general concept of clique-width of relational structures by Blumensath and Courcelle (2006). We also relate the new notion to monadic second-order logic of point configurations. As an application, we provide several linear FPT time algorithms for geometric point problems which are NP-hard in general, in the special case that the input point set is of bounded clique-width and the clique-width expression is also given.
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